Resolve and Expand

Mapping Conformant Planning into SAT Through Compilation and Projection

“…Our scheme for conformant planning can be easily adapted for solving QBFs of this form; indeed, provided that φ is compiled in d-DNNF, the existential variables f i 's can be eliminated by projection, the universal variables s 0 's can be eliminated by conditioning and conjoning as in (5), and finally the existential plan variables can be solved by a single SAT call over the resulting formula. This method for solving QBFs is related to the 'resolve' and 'expand' technique recently proposed by Biere in [10]. Indeed in QBFs of the form ∃plan ∀s 0 ∃f i φ, Biere eliminates the existential f i variables by resolution, and the universal s 0 variables by an expansion that is similar to the one captured in (5).…”

“…The experiments that are reported show that this compile-project-sat planner is competitive with state-of-theart optimal conformant planners and improves upon a planner recently reported at ICAPS-05 [8]. The proposed techniques seem to apply also in direct fashion to the solution of QBFs of the form ∃x ∀y ∃z φ which are in correspondence to the problem of verifying the existence of conformant plans for a given horizon [9], and are related to the 'resolve' and 'expand' methods for solving QBFs recently proposed in [10].…”

“…The form of the theory T cf (P ) in (5) is also closely related to the 'resolve' and 'expand' technique for solving QBFs recently proposed by Biere in [10]. Indeed in QBFs of the form ∃plan ∀s 0 ∃f i φ, Biere eliminates the existential f i variables by resolution, and the universal s 0 variables by expansion.…”

On Conflicts and Strategies in QBF

“…In one approach, a solver traverses the search space, while pruning it by propagation, similarly to SAT solvers [30,31,19,21,12,22]. In the second approach, a solver eliminates (expands) quantifiers obtaining thus a SAT problem [26,6,20,3].…”

“…Some solvers traverse the search space by assigning values to the individual variables similarly as a backtracking algorithm would [30,11,21]. Other solvers expand quantifiers into logical connectives according to their semantics [20,6,14]. In this paper we aim to bridge this dichotomy by guiding quantifier expansion by conflicts found by traversal.…”